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*                        Ramsey Model                      *
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 Sets
 t   time     / 0*98 /
*** Cannot make t larger due to demo version restrictions
 T0(t) initial time
 T1(t) final time;

 T0(T) = yes$(ord(t) eq 1);
 T1(T) = yes$(ord(t) eq card(t));

 Scalars
 a                                /5.0/
 k                                /3.0/
 b     initial capital            / 15.0  /
 x0                              /0.0/
 x1                              /100.0/

 Variables
 u(t)  production output
 x(t)  capital stock
 j     utility;

 Parameters
 f(u) function
 f(u) u\(a*(1+u\k))        

 Equations
 kk(t) capital stock balance
 jj    objective function;

 kk(t+1)..  x(t+1) =e= f(u) - g(x);
 jj..  j =e= sum(t, u(t));

*** Initial values and constraints
 x.fx(T0)=x0;
 x.fx(T1)=x1;
 u.lo(t)=0;

*** Turn off unnesessary listing
 option solprint = off;
 option limrow = 0;
 option limcol = 0;

 Model growth / all /;
 Solve growth maximizing j using nlp;

*** Show the results
 display x.l, u.l;


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* Download gnuplotxyz library to draw graphs
* (http://www.uni-hamburg.de/Wiss/FB/15/Sustainability/schneider/gnuplot/)
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 Parameter PLOT_1 data for plotter;
 PLOT_1("graph",t,"y")=c.l(t);
 PLOT_1("graph",t,"x")=ord(t);

$libinclude gnuplotxyz PLOT_1 x y